So, your track is literally on the opposite side of the ball from the fingers/thumb? In general I think a low track comes from turning the wrist early and/or not having a strong enough wrist position. If your track is as low as it sounds, you might be turning early and you might have you thumb on top of the ball at the same time you're releasing. This is just speculation.
That said, you shouldn't really think about turning your fingers. Having the fingers behind and under the ball should at least provide moderate axis rotation(what you call "side turn") on its own. The fingers under the ball means the fingers are under an imaginery line horizontally through the center of the ball(from straight behind). I think the way you create more side rotation is to position your hand so that the fingers are more on the left side of the ball going into the release(for a right hander, this is called working the inside of the ball). I think about pointing with the index finger or putting the ball's weight on the pad of the index finger. The rotation of the fingers around the ball should happen naturally, more or less.
JAnderson from this site likes to have people think of a thumb position(I believe) going into the release and during the follow through. For example, from behind the bowler, the thumb pointing at 12 oclock going into the release and the thumb pointing at 10 oclock in the follow through would provide some side rotation. Thumb pointing at 9 oclock in follow through would be more side rotation. I believe that's how it works. Personally I'm not good at that, I prefer to let the hand do what it wants to do, or I lean more towards staying behind the ball. I'm never rotating all the way to 3 with my fingers, most likely the furthest I would go is about 4/5. The starting position basically dicatates the side rotation for me.
Hope this gives you some helpful information.
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